UV Maps - is it possible to use the third channel (W?)
Looking into the Blender source code, the UV processing does not account for the third channel - so this is not possible within a single standard UV map. In order to store an additional (W) channel you could use an additional UV map - eg, 'UVMap1' could hold U and V while the 'U' channel of 'UVMap2' could hold the 'W' channel. However, this method does not provide a simple method of manipulating the UVW map (since the W channel needs to be manipulated separately.

That said, by considering the two UV maps as a 'front view' and a 'side view' of UVW space we can achieve a similar effect - but you need to be careful when manipulating the UV maps to ensure they stay consistent.

To demonstrate, start with your initially unwrapped mesh - a standard UV map :



Copy the UV map (click the '+' alongside the list of UV maps in Edit mode) and rename them to make it clear that one is the UV "front" view and the other is the 'WV' "side" view. 'Select all' (A), scale to zero in the X-axis (SX0Enter) and select everything and move it to the size (GX then drag to the side). You should now have something like this :



Now to move points into the W dimension you can simply select them (or select a whole face) and drag them along the X (U) axis with GX.



To combine the separate 'front' and 'side' UV maps into a UVW map you simply need to separate the channels and re-combine into a single UVW vector :